Efficient method to compute $\mathbb{Z}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$

Abstract

We propose an efficient method to numerically evaluate $\mathbb{Z}_4$-indices of Möbius/hourglass topological phases with glide symmetry. Our method directly provides $\mathbb{Z}_4$-indices in the lattice Brillouin zone while the existing method requires careful observations of momentum dependent Wannier charge centers. As applications, we perform systematic computation of $\mathbb{Z}_4$-indices for Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$. In particular, our analysis elucidates that $\mathrm{UCoGe}$ shows strong Möbius superconductivity for the $A_u$- or $B_{3u}$-representation whose topology has not been fully characterized. Furthermore, obtained phase diagrams reveal novel topological gapless excitations in the bulk which are protected by nonsymmorphic glide symmetry. We observe these gapless excitations with glide symmetry by doping holes into the superconducting phase of the $B_{1u}$- or $B_{3u}$-representation.